1. Field of the Invention
The present invention relates to assemblies for translating rotational motion to reciprocal harmonic linear motion; in particular, connecting rod assemblies for internal combustion engines. The present invention also relates to assembly for translating two planar objects with respect to each other while maintaining a constant distance between the two planar objects, and an assembly for walking while maintaining a support position at a uniform distance above the surface being walked upon.
2. Description of the Related Art
Conventional reciprocating internal-combustion engines include a block having cylinders, a rotating crankshaft, and one or more pistons, which move in linear, reciprocating motion in the cylinders, connected to the crankshaft by connecting rods. The structure and operation of conventional internal-combustion engines is well known, and has been described in, for example, The Internal-Combustion Engine in Theory and Practice, Charles Fayette Taylor, the M.I.T. Press, copyright 1968 and 1985.
The crankshaft is mounted to the block so that the crankshaft rotates about a crankshaft-rotation axis. Each cylinder in the block has an axis which passes through the crankshaft-rotation axis. The crankshaft has one or more crank pins having a crank pin axis which is substantially parallel to and spaced a distance r from the crankshaft-rotation axis; thus, r defines the radius of the circle circumscribed by the crank pin. The angular position of the crank pin is measured by the angle .theta. from top dead center (tdc), and the angular velocity d.theta./dt of the crank pin is expressed as .omega.. The length of the connecting rod is l.
The mass m which is considered to reciprocate with the piston includes the piston, the piston rings, the piston pin (which attaches the piston to the rod) and the equivalent mass of the upper end of the connecting rod.
A conventional connecting rod has a finite length l which causes harmonic accelerations of the reciprocating mass (i.e., the piston), resulting in primary, secondary, and higher order harmonic unbalanced forces along the piston axis. The forces are given by equation (1): EQU F=m.omega..sup.2 r[cos .theta.+(r/l)a.sub.2 cos 2.theta.+(r/l)a.sub.4 cos 4.theta.+higher order terms] (1)
Equation (1) describes a primary unbalanced force varying in amplitude with crankshaft rotation and a secondary unbalanced force varying at twice the crankshaft speed and higher order forces varying at higher even multiples of crankshaft speed. The coefficient a.sub.2 in the secondary force component of equation (1) is .perspectiveto.1, and the frequency of the secondary force is twice the frequency of the primary force.
Because of space considerations, a typical modern engine has an r/l ratio ranging from about 0.2 to about 0.33, resulting in secondary inertial forces having an amplitude of 1/5 to 1/3 of the amplitude of the primary inertial forces. As the ratio r/l approaches zero, the secondary and higher order inertial forces disappear and the piston motion approaches that of simple harmonic motion. Accordingly, one approach to remove the higher order forces is to increase l so that r/l approaches zero. However, the space considerations make this solution impractical.
FIGS. 1A and 1B schematically illustrate the .theta.=0.degree. and the .theta.=90.degree. orientations of a conventional engine including a crankshaft 20, a piston 22, and a connecting rod 24. In essence, the y-separation distance between the crank pin 26 and the piston 22 is not fixed; the variation in this distance depends on factors including the length l of the connecting rod, and the angle .psi. between connecting rod 24 and the cylinder axis 25, where the cylinder axis 25 is defined as the axis of connecting rod 24 when .theta.=0. As the crank pin 26 moves in a circular path of radius r, the Y-separation distance between the crank pin 26 and the piston 22 varies between a maximum value Y.sub.MAX equal to l at .theta.=0.degree. and .theta.=180.degree. a minimum value Y.sub.MIN equal to .sqroot.l.sup.2 -r.sup.2 at .theta.=90.degree.. The difference between these two extreme values divided by the full piston stroke 2r corresponds to the percent maximum variation %.DELTA.Y of the Y-separation distance with respect to the total travel distance of the piston and is given in equation (2): ##EQU1## When the value %.DELTA.Y is zero, the Y-separation distance is constant (corresponding to case of an infinitely long connecting-rod 24) and the piston 22 moves in simple harmonic linear motion in response to the uniform rotation of the crankshaft 20.
For r/l=0.2 %.DELTA.Y=5.05 and for r/l=0.33 %.DELTA.Y=8.48.
In engine design, one of the main constraints influencing the number and placement of (i.e., configuration) of the cylinders in a multi-cylinder engine is satisfactory balancing of the axial forces produced by the reciprocating mass in each cylinder. When many cylinders are adjacent to each other, the primary forces, and sometimes also the secondary forces can be made to cancel each other when certain fixed phase relationships and spatial relationships between the reciprocating masses exist. Unbalanced moments associated with these forces result when the axes of any two adjacent cylinders do not lie along the same line and thus the forces do not have the same line of action. The primary and secondary moments can also be eliminated in some cases by adding additional pairs of cylinders. For example, the conventional in-line, 4-cylinder, 4-cycle engine utilizes a symmetrical crankshaft such as the crankshaft shown in FIG. 3, which results in cancellation of the primary forces and the primary and secondary moments, but not the secondary forces which reinforce each other producing a large resultant second-order shaking force in the engine.
An engine is balanced by eliminating as many forces and moments as possible, and by the proper combination of crankshaft design, number of cylinders and cylinder arrangement. Common cylinder arrangements or configurations include in-line engines, horizontally-opposed engines, "V", "X", "W", and "H" type engines, and radial engines. Whatever the arrangement, it is unusual to have more than six or eight cylinders in a row because of torsional vibrations in the crankshaft which even for short crankshafts can become severe at certain critical engine speeds. Primary, secondary, and higher harmonic torsional vibrations occur as a result of the inertia of the reciprocating mass doing work on the crankshaft. The inertia torque applied to the crankshaft is given by equation (3). EQU T=m.delta..sup.2 r.sup.2 [t.sub.1 sin .theta.+t.sub.2 sin 2.theta.+t.sub.3 sin 3.theta.+higher order terms] (3)
The inertia torque coefficients t.sub.n are zero only when r/l=0, except the second order coefficient t.sub.2 which is the only torque present in the case of simple harmonic motion. To date, balancing of the primary and secondary forces and moments has been accomplished in the following engine designs: in-line engines with 6 or 8 cylinders or more; horizontally-opposed engines with 8 or 12 cylinders or more; "V" type engines with 12 or 16 cylinders or more; "V" type engines with 8 cylinders (with counter-weighted crank); radial engines (with two counter-rotating counter-weights); and "W" type engines with 16 cylinders or more.
In normal operation of an internal combustion engine, as a spark is discharged to initiate the beginning of the combustion of the air-fuel mixture, the piston approaches the end of the compression stroke. Since combustion takes a finite time, the mixture is ignited during the compression stroke before the piston reaches top dead center (btdc). This results in a pressure rise associated with combustion before the end of the compression stroke, and an increase in the compression (negative) work. Advancing the timing allows the pressure rise associated with combustion to reach its peak at an optimum crank angle of .theta.=5.degree.-20.degree. after top dead center (atdc) and thus causes the expansion (positive) work to increase. However, advancing the timing also increases the pressure during the compression stroke which in turn causes the compression (negative) work to increase. A trade-off between the btdc timing of the apark and the atdc timing of maximum pressure leads to an optimum ignition timing.